Question:
Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.
Correct Answer
$7800
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 8%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5000 × 8% × 7
= $5000 ×8/100 × 7
= 5000 × 8 × 7/100
= 40000 × 7/100
= 280000/100
= $2800
Thus, Simple Interest = $2800
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $2800
= $7800
Thus, Amount to be paid = $7800 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5000
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5000 + ($5000 × 8% × 7)
= $5000 + ($5000 ×8/100 × 7)
= $5000 + (5000 × 8 × 7/100)
= $5000 + (40000 × 7/100)
= $5000 + (280000/100)
= $5000 + $2800 = $7800
Thus, Amount (A) to be paid = $7800 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5000, the simple interest in 1 year
= 8/100 × 5000
= 8 × 5000/100
= 40000/100 = $400
Thus, simple interest for 1 year = $400
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $400 × 7 = $2800
Thus, Simple Interest (SI) = $2800
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $2800
= $7800
Thus, Amount to be paid = $7800 Answer
Similar Questions
(1) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?
(2) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.
(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?
(5) If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.
(9) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
(10) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.